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 A218360 Minimal order of degree-n irreducible polynomials over GF(13). 4
 1, 7, 9, 5, 30941, 63, 5229043, 32, 27, 11, 23, 45, 53, 29, 4651, 64, 103, 19, 12865927, 25, 43, 161, 1381, 288, 701, 371, 81, 145, 1973, 31, 311, 128, 207, 721, 211, 37, 1481, 90061489, 79, 41, 6740847065723, 261, 119627, 115, 181, 47, 183959, 576, 1667, 101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) < 13^n. LINKS Max Alekseyev, Table of n, a(n) for n = 1..416 Eric Weisstein's World of Mathematics, Irreducible Polynomial Eric Weisstein's World of Mathematics, Polynomial Order FORMULA a(n) = min(M(n)) with M(n) = {d : d|(13^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}. a(n) = A218337(n,1) = A213224(n,6). MAPLE with(numtheory): M:= proc(n) M(n):= divisors(13^n-1) minus U(n-1) end: U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end: a:= n-> min(M(n)[]): seq(a(n), n=1..33); MATHEMATICA M[n_] := M[n] = Divisors[13^n - 1]~Complement~U[n - 1]; U[n_] := U[n] = If[n == 0, {}, M[n]~Union~U[n - 1]]; a[n_] := Min[M[n]]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Oct 24 2022, after Alois P. Heinz *) CROSSREFS Cf. A213224, A218337. Sequence in context: A132715 A154910 A063603 * A020788 A198921 A099877 Adjacent sequences: A218357 A218358 A218359 * A218361 A218362 A218363 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 27 2012 STATUS approved

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Last modified June 7 21:29 EDT 2023. Contains 363157 sequences. (Running on oeis4.)